probability question, not easy

Hello to everyone. I want to find a solution to the following general problem:

Given a random event has a probability of 1/n, how many trials are required so that the actual frequency of the event to be 1/n +/-ERROR.
Let's say EROR to be 5%. I know that in n trials the probability of occuring at least once is 1-1/e, but this doesn't help me.


Thanks,
Andrei

Quote: andreic555

Hello to everyone. I want to find a solution to the following general problem:

Given a random event has a probability of 1/n, how many trials are required so that the actual frequency of the event to be 1/n +/-ERROR.
Let's say EROR to be 5%. I know that in n trials the probability of occuring at least once is 1-1/e, but this doesn't help me.

You can only calculate the number of trials required for the actual frequency to be 1/n +/- ERROR with certain probability (which is always <100% unless number of trials is infinite), so you could ask for example:

Given an event with probability of 1/n, how many trials are required for the actual frequency to be 1/n +/- 5% with 95% probability?

You reformulated the question well. This is what I want to calculate. But i don't know how.

Of course the probability of the frequency to reach the desired interval is always less than 1.

Thanks.